The determination of molecular weights and sizes from light scattering measurements has been an important procedure since the mid-1940's. The general method for making these determinations was established by Zimm [J. Chem. Phys. 16, 1099 (1948)] and consists of preparing a series of molecular suspensions, each at a different concentration, and then measuring the excess scattering of each suspension as a function of scattering angle. From these measurements and numerical extrapolations of the data to zero scattering angle and zero concentration, the so-called weight-average molecular weight, M.sub.w, z-average square radius, &lt;r.sub.g.sup.2 &gt;, and second viral coefficient, A.sub.2, are determined for the molecules in the suspension. The second quantity is often referred to as the mean square radius or by the misnomer square "radius of gyration."
At very low concentrations, c, the weight-average molecular weight M.sub.w of molecules in a suspension may be derived from measurements of the suspension's light scattering properties by ##EQU1## where the excess scattered intensity ratio at each scattering angle .theta. EQU R(.theta.)=f[I(.theta.)-I.sub.s (.theta.)]/I.sub.0. (2)
Here I(.theta.) is the measured intensity of scattered light from the suspension at an angle .theta., I.sub.s (.theta.) is the corresponding quantity for the pure solvent, I.sub.0 is the incident light flux, and f is an absolute calibration constant. The second virial coefficient is A.sub.2. For vertically polarized incident light of vacuum wavelength .lambda..sub.0, the constant EQU K*=(2.pi.n.sub.0 dn/dc).sup.2 /(N.lambda..sub.0.sup.4), (3)
where N is Avogadro's number, n.sub.0 is the refractive index of solvent and the refractive index increment is dn/dc. This latter quantity represents the change of solution refractive index, dn, for a change of molecular concentration dc.
Debye showed in general that the angular intensity variation, P(.theta.), is of the form EQU P(.theta.)=1-.alpha..sub.1 x+.alpha..sub.2 x.sup.2 -.alpha..sub.3 x.sup.3 +. . . , (4) EQU where EQU x=(2k sin .theta./2).sup.2, (5)
and k=2.pi.n.sub.0 /.lambda..sub.0. The leading coefficient, .alpha..sub.1, is easily shown to be EQU .alpha..sub.1 =&lt;r.sub.g.sup.2 &gt;/3, (6)
where the square mean radius, or z-average square radius, is given by ##EQU2## the integration being taken over all mass elements dM of the molecule with respect to its center of gravity.
Zimm considered the reciprocal form of Eq. (1) at small values of u in the form ##EQU3## The parameter u=&lt;r.sub.g.sup.2 &gt;x/3 is always small in the limit as sin.sup.2 .theta./2--&gt;0. Note that in the limit as c goes to 0 and u--&gt;0, setting y=K*c/R.sub..theta. EQU y.sub.0 =K*c/R(0)=1/M.sub.w, (9)
i.e. the intercept yields the reciprocal weight average molecular weight. Setting y=K*c/R(.theta.), we note further that in the limit as c--&gt;0, EQU dy/d(sin.sup.2 .theta./2)=(2k).sup.2 (r.sub.g.sup.2)/(3M.sub.w),(10)
i.e. the initial slope of the extrapolated c=0 data will yield the z-average square radius directly when Eq. (10) is combined with Eq. (9). In addition, in the limit as sin.sup.2 .theta./2--&gt;0, EQU dy/dc=2A.sub.2, (11)
i.e. the initial slope of the extrapolated sin.sup.2 .theta./2=0 data will yield the second viraial coefficient. Zimm implemented these results graphically by means of the so-called Zimm plot technique. The process consists of plotting the experimentally measured values of K*c/R(.theta.) against sin.sup.2 .theta./2+Sc, where S is an arbitrary "stretch" constant selected for convenience in making the plots so that the Sc values are comparable in magnitude to the sin.sup.2 .theta./2 values.
Historically, these measurements have been difficult to perform because of the requirement that the prepared solutions be essentially free of dust. The presence of even minute amounts of dust often can result in spurious scattering that may overwhelm the scattering signals of the molecules themselves, especially in the forward scattering directions. The most time consuming elements of the light scattering measurement process is preparing the series of molecular dilutions, each free of dust. While the light scattering measurements themselves may only require a few minutes using modern multiangle light scattering photometers, the sample preparation may require manny hours or even days.
With the introduction of size exclusion and other types of chromatography which are combined with an in-line multiangle light scattering detector, it has become possible to measure the weight-average molecular weight and z-average square radius for each eluting fraction as long as the corresponding concentration of each fraction is known. This is usually achieved by an in-line concentration detector. The chromatographic separation is achieved by means of a packed column, for the ease of size exclusion chromatography, or a channel with an externally applied transverse field, for the case of field flow fractionation chromatography, etc. Only a single concentration is required to be injected in the chromatographic procedure, with the column or channel separating the sample, for example, by the hydrodynamic size of its molecular constituents. These techniques are quite useful in removing the effects of dust since dust, generally being of a greater size than the molecules, is separated and isolated from the molecules by the column. Most importantly, however, preparation of only a single concentration is required which is much easier to preparae than an entire series. Although such chromatographic separation can provide further information about the molecules, such as mass and size distributions, this detail may not be required for many applications. In addition, the chromatographic separation per se requires an injector, column, light scattering detector, and concentration detector, together with several chromatographic system elements such as pumps, filters, dampers, etc.
A simple method for determining weight average molecular weights, z-average square radii, and second virial coefficients has been developed that combines some elements of on-line chromatographic separation with the standard batch sample procedures described by Zimm. Although the concept of injection of a sample without a column seems to be an attractive means to produce a concentration gradient by dilution, with an in-line light scattering detector and an in-line concentration detector being used to provide the light scattering data at the several concentrations required for application of the Zimm technique, the concept has two basic shortcomings. First is the problem that during flow through a capillary or channel, a molecular sample may separate somewhat on the basis of the hydrodynamic radii of its constituents and the laminar flow of the stream. The molecular weight distribution must be identical in each eluting fraction (at each concentration) for application of the method. The second major obstacle to implementing this injection method is the so-called band broadening effect. Because of continuous dilution effects during the sample flow from the injector through the light scattering detector and through the concentration detector, the concentration profile will not match the light scattering profile. Because of these so-called band broadening effects, the derived concentration profile of the diluted eluting sample would not be accurate.
Many others have used light scattering measurements for the on-line characterization of particulates. These include Takeda, et al. in U.S. Pat. No. 4,957,363 who describe the use of multiwavelength measurements on flowing samples; Webb, et al. in U.S. Pat. No. 4,664,513 who describe seeding a flowing stream with reflective spherical particles to monitor local vorticities via the light scattering of the particles; Hattori in U.S. Pat. No. 4,264,206 who describes a dust counter based on measuring scattered light from particles in an air stream; Wertheimer in U.S. Pat. No. 4,265,538 who describes a special flow cell for making light scattering measurements at three mutually orthogonal directions from a flowing stream; and, Steen, in U.S. Pat. No. 4,915,501 who describes a flow cytomer strucutre permitting measurement of light scattered into two different angular ranges from microscopic particles and biological cells.
In his U.S. Pat. No. 3,850,525, Kaye describes means to measure the scattering of light into two directions from a small sample that may be measured in a static or flowing mode. He also discusses how these measurements combined with Zimm's implementation may be used to determine molecular parameters. Chu, in his U.S. Pat. No. 4,565,446, describes a cell configuration whereby scattered light may be measured from a fluid passing therethrough at two scattering angles. He also discusses requirements for making Zimm plots from samples at different angles. Neither of the two aforementioned patents discloses means for making on-line Zimm plots, but only the need to make measurements in the absence of background and efforts to reduce said background interferences.
The basic U.S. Pat. No. 3,522,725 of Waters describes common operating principles of liquid chromatographs. He does not discuss Zimm plots nor their posssible implementation in his chromatrographic instrument since it does not contain light scattering and detection means. The inclusion of a refractive index detector, a standard element often used to monitor molecular concentrations, is disclosed together with the special environmental contraints required to ensure that its output remains stable.